Question: Add $175_{9} + 714_{9} + 61_9$.  Express your answer in base $9$.
Answer: When summing these three numbers, we notice that $5 + 4 + 1$ leaves a residue of $1$ when divided by $9$, so it follows that the sum has a rightmost digit of $1$ and that carry-over must occur. After carrying over to the next digit, we must find the sum of $1 + 7 + 1 + 6 = 16_9$, which leaves a residue of $6$ when divided by $9$. Thus, we write down $6$ as the next digit and carry-over another $1$. Evaluating the next digit, we must find the sum of $1+1+7 = 10_9$, which leaves a residue of $0$ when divided by $9$. Thus, we must carry-over one more time, yielding that: $$ \begin{array}{c@{}c@{\;}c@{}c@{}c@{}c} & & & \stackrel{1}{1} & \stackrel{1}{7} & \stackrel{}{5}_{9} \\ & & & 7 & 1 & 4_{9} \\ &+ & & & 6 & 1_{9} \\ \cline{2-6} && 1 & 0 & 6 & 1_{9} \\ \end{array} $$Thus, the answer is $\boxed{1061_{9}}$.

Alternatively, we can notice that $175_9 + 714_9 = 1000_9$, so $1000_9 + 61_9 = 1061_9$.